The Influence of Ca Content on the Current Density of the Superconducting Y1−xCa x Ba2Cu3O7−δ Compound

Abstract

In this research, we study the effect of Ca content on charge transfer mechanism of YBa2CU3O7−δ compound, for composition Y1−xCaxBa2Cu3O7−δ (x=0, 0.05, 0.1, 0.2). Substitution of Ca changes the charge content, and as a result, potential energy changes; this will lead to structural changes (positions of ions and distances between them); this also leads to variations in Cu 2–O 3 and Cu 2–O 2 bond lengths and the effective coordination of Cu 2 with respect to oxygen ions. Starting from zero Ca content, the positions and distances for all ions in the crystal were calculated for all Ca concentrations. Moreover, the charge transfer mechanism from CuO chains to CuO 2 planes was studied and also the effective hole-doping dependences P(x) on bond valence sum. The hole concentration, energy gap, and current density, in Y1−xCaxBa2Cu3O7−δ (where x=0.1 to x=0.2) have been calculated, assuming that the net doping of CuO 2 layers is the sum of contributions from CuO chains and from substitution of Y 3+ by Ca 2+. Applying the concept of bond valence sum model for the calculation of the hole concentration in the CuO 2 plane. The model proposed assumes that the oxygen valence sum and Cu(2) valence sum influence the hole concentration in the CuO 2 plane and as a result on the hole conduction in the crystal. These p(x) dependences are combined with universal (parabolic) phase relation Tc(p). Thus, current density may be calculated considering the Ca concentration effect according to one of the following equations: $$\begin{array}{@{}rcl@{}} J=2.22e~\ast~\sqrt{\frac{E_{\mathrm{g}}}{m}}\langle 0.16 + 0.11 \sqrt{1-\frac{T_{c}}{T_{c \max}}\rangle},\\ J=2.22\ast\,e\, \sqrt{\frac{E_{g}}{m}}\langle 0.16 + \frac{n_{\text{Ca}}}{\mathrm{2}}-(7-\delta)\rangle \end{array} $$ Here, Tc and Eg were calculated as a function of Ca content.